Equations of attainable set dynamics, part 1: integral funnel equations
Journal of Optimization Theory and Applications
Reachability Analysis Using Polygonal Projections
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Global Optimization with Nonlinear Ordinary Differential Equations
Journal of Global Optimization
Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
SIAM Journal on Scientific Computing
Validated solutions of initial value problems for parametric ODEs
Applied Numerical Mathematics
On Taylor Model Based Integration of ODEs
SIAM Journal on Numerical Analysis
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
Technical Communique: Nonlinear bounded-error state estimation of continuous-time systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Hi-index | 22.14 |
The computation of rigorous enclosures of the reachable sets of nonlinear control systems is considered, with a focus on applications for which speed is crucial. Low computational costs make interval methods based on differential inequalities an attractive option. Unfortunately, such methods are prone to large overestimation and often produce useless results in practice. From physical considerations, however, it is common that some crude set is known to contain the reachable set. We establish a general bounding result, based on differential inequalities, which enables the effective use of such sets during the bounding procedure. In the case where this set is a convex polyhedron, an efficient implementation using interval computations is developed. Using readily available physical information from practical examples, this method is shown to provide significant advantages over alternative methods in terms of both efficiency and accuracy.